Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 20

trade-off between model uncertainties and measurement errors are well developed
but still not frequently used [24, 35]. Dynamic methods have been proposed and are
being developed [36-40], but applications of those are not documented.
Other topics are related to data reconciliation, such as sampling error and recon-
ciliation criterion weighting factor evaluation [41, 79, 96], reconciled value accuracy
evaluation [44], use of reconciled values to calculate and display plant performance
indices, such as concentrate grade and recovery. Owing to their better reliability,
these indices may improve manual or automatic process performance optimization
[45, 46]. Coupling of dynamic reconciliation with control has also been investigated
[47, 48], as well as gross error detection, fault isolation and diagnosis [49, 50]. Fi-
nally, instrumentation design can be performed on the basis of data reconciliation
methods used as process observers [51, 52].
The chapter includes the following parts. Section 2.2 begins with definitions of
plant process variables and operating regimes that may be considered in reconcil-
iation methods. Then, in Section 2.3, mass and energy conservation equations are
written for different plant operating modes. As is the case for all the sections of this
chapter, strong emphasis is placed on mass balance problems, rather than on energy.
Then, since the basic incentive for reconciling data is the presence of measurement
errors, Section 2.4 covers measurement problems, while Section 2.5 presents the
observation equations. Section 2.6 introduces the general principles of data recon-
ciliation algorithms based on least-squares procedures, while Section 2.7 gives the
steady-state and stationary operating regime solutions for the linear constraints case.
Section 2.8 briefly discusses the non-linear reconciliation cases. Section 2.9 is de-
voted to the reliability of reconciled data analysis. Section 2.10 presents some rec-
onciliation methods for plants operating in the dynamic regime, while Section 2.11
briefly addresses the issue of how reconciliation methods can help to improve met-
allurgical plant instrumentation design strategies. Section 2.12 explores how mass
and energy conservation constraints can also be used for detecting abnormal pro-
cess behaviors or measurement problems. Finally Section 2.13 makes way for the
integration of reconciliation techniques into optimization or control loops.

2.2 Process Variables and Operating Regimes

Variables involved in mineral processing units characterize process states relatively
to material quantities (extensive properties) or qualities (intensive properties). Mass
or volume flowrates and hold-ups of solid, liquid, slurry and gas phases (or of given
species within these phases) belong to the first category, as well as other related
variables such as levels and flowrates. The second category frequently includes the
following variables:
•

concentrations of chemical species or minerals in solid, liquid and gaseous
phases;

• solid percentage in slurries;

• particle size and density distributions;